Question: Rewrite as a simplified fraction. ${2.\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}10x &= 23.3333...\\ 1x &= 2.3333...\end{aligned}}$ Subtracting the two equations, we have: ${9x = 21}$ ${x = \dfrac{21}{9}} $ ${x = \dfrac{7}{3}} \text{or} {2 \dfrac{1}{3}}$